Yes. I think that feral dogs and cats should be euthanized. I don't like shelter animals being "rescued" just because they are on death row. Adopting a pet for ones own self or family and rescuing an animal to foster it, or to place it in foster, is completely different. If you want a pet and choose to get one at a shelter, by all means do it. I am all for that. What I don't like is someone "rescuing" said animal only because it's going to be put down, just to turn around and rehome it. So many of the animals in shelters are repeat tenants. I have seen dogs that have been "rescued" and then returned several times. This is not fair and I think the animal is better off euthanized.
If you have no plans on breeding a pet dog or cat, or if you let them roam free, then yes I think that by law you should have to spay/neuter them. Not only does it keep the stray population down but it lengthens their life span.
As far as the dogs/cats in Iraq/Afghanistan goes. There is a lawful command that is in place that says that no soldier can keep or care for a wild animal.MOD 10 of the CENTCOM Individual Protection and Individual/Unit Deployment Policy, states that local animals are carriers of multiple diseases, to include rabies, and that deployed personnel will avoid contact with local animals and are not to feed, adopt or interact with them in any way.
Subordinate commanders have issued feral animal policies that reinforce this policy. Afghanistan Policy Letter 25, Feral Animal Control on FOBs/COBs, provides guidance to all personnel assigned to U.S. Forces in Afghanistan and directs commanders at all levels to enforce General Order 1B, which prohibits adoption of pets and mascots, implements animal control practices, requires proper procedures to prevent animal access to sources of food waste, and forbids compassionate feeding of animals in the deployed environment.